Skeleton approximations of optimal stopping strategies for American type options with continuous time (Q2740080)

This paper deals with the optimal stopping buyer strategies for American type options. The structure of optimal stopping strategies is investigated by applying the direct probabilistic analysis under general assumptions for underlying pricing processes. The model of pricing process is a two component inhomogeneous in time Markov process \((S_{t},I_{t})\) with phase space \([0,\infty)\times Y\). The first component is the corresponding pricing process and the second component (with general measurable phase space \(Y\)) represents some stochastic index process controlling the pricing process. The authors study the skeleton type approximations for continuous time pricing processes. The explicit upper bounds for the step of discretization for the \(\varepsilon\)-optimal stopping strategies are found and a constructive description of the \(\varepsilon\)-optimal stopping strategies for American type options with continuous time is presented.